A study of sedimentation problems in the lower reaches of the river Österdalälven

IN

DEGREE PROJECT ENVIRONMENTAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2018,

A study of sedimentation problems in the lower reaches of the river Österdalälven

LOUISE SJÖLUND

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

TRITA -ABE-MBT-18375

www.kth.se

A study of sedimentation problems in the lower reaches of the river

Österdalälven

Louise Sjölund

Supervisor Bijan Dargahi

Examiner

Anders Wörman

Degree Project in AF283X (Environmental engineering and sustainable infrastructure) KTH Royal Institute of Technology

School of Architecture and Built Environment

Department of Sustainable Development, Environmental Science and Engineering

SE-100 44 Stockholm, Sweden

i

Abstract

The river Österdalälven deposits large amounts of sediment when it passes through the city of Mora. The sediment deposition risks clogging the inlet to the lake Siljan, hampers navigation, and creates a risk of the river forming new channels. This study has addressed the problem by creating a numerical 2D depth- averaged combined hydrodynamic and sediment transport model of the reach. The study focused on the mechanisms behind the sedimentation and erosion patterns. River training structures in the form of groynes were added to the model to investigate whether mitigation of the problem by physical structures was possible. Because of the lack of field data, some of the flow and sediment transport parameters had to be estimated. Sensitivity analyses were performed to analyse the model’s response to the choice of boundary conditions, input parameters, and auxiliary models. The study concluded that erosion occurs in areas where the shear stress or flow velocity is high and sedimentation in areas with flow circulation and lower flow velocity. The sediment yield at the problem area, i.e. at the mouth in Siljan was flow-

dependent and increased with larger flow discharges. The yearly sediment yield was low compared to stations downstream. The model was sensitive to the choice of boundary conditions, Manning’s

roughness coefficient, and sediment transport mode and transport capacity formula. The main conclusion was that it is crucial to collect the relevant field data to obtain more reliable result for further studies. It was further concluded that physical structures in the form of groynes could decrease the amount of sediment that deposits at the mouth of Österdalälven in Siljan. The study has shown that it is possible to create a working numerical river model based on the physical understanding of the flow despite the lack of field data.

ii

Sammanfattning

Österdalälven avsätter stora delar sediment när den passerar genom Mora. Sedimentavsättningarna riskerar att täppa igen inflödet till sjön Siljan, hindrar navigation samt ger upphov till en risk att älven bryter igenom och skapar nya kanaler. I denna studie har en tvådimensionell medeldjupsmodell för hydrodynamik och sedimenttransport av Österdalälvens sträckning som passerar Mora skapats. För att undersöka om sedimentavsättningen kunde minskas med hjälp av fysiska strukturer testades modellering med erosionskyddet hövder. Då fältdata var begränsad har vissa parametrars värde uppskattats och studien har därmed fokuserat på mekanismen bakom sedimenteringen och erosionen. Känslighetsanalyser av modellen har gjorts för att undersöka hur känslig modellen var till val av randvillkor, parametrar och hjälpmodeller. Det kunde konstateras att erosion sker i områden med hög flödeshastighet och hög skjuvhållfasthet och sedimentering i områden med cirkulation och låg flödeshastighet.

Sedimenttransporten i problemområdet vid mynningen i Siljan var beroende av flöde och ökade med ett ökat flöde. De årliga transporterade mängderna sediment var lägre än vid mätstationer nedströms Mora.

Modellen var känslig till val av randvillkor, Mannings tal, samt till val av transportsätt och

transportkapacitets-formel för sediment. Den viktigaste slutsatsen var att för att förfina modellen till att på ett pålitligt sätt kunna kvantifiera de relevanta aspekterna av hydrodynamik och sedimenttransport krävs att relevant fältdata samlas in. Därutöver visade studien att fysiska strukturer i form av hövder kunde minska mängden sediment som avsätts i flodmynningen i Siljan. Slutligen drogs slutsatsen att det är möjligt att skapa en fungerade numerisk modell baserat på de fysikaliska flödessambanden trots avsaknaden av fältdata.

Key words

Österdalälven, sedimentation, sediment transport, erosion, hydraulic modelling, river modelling, river training.

iii

Acknowledgements

I would like to express my gratitude to my supervisor Bijan Dargahi for his dedicated and enthusiastic guidance in this project.

iv

List of figures

Figure 1. Photos of the sandbanks by anonymous photographer (personal communication with B.

Dargahi, 2018) deposited on the island Sandholmen in Siljan. For the location of the island in the lake, see Figure 4. ...2 Figure 2. Map retrieved from B. Dargahi (personal communication, 2018) of the reach showing depth (light to dark blue), areas where dredging (dashed red area), and beach protection have been performed (red dots). The volume of removed sediment is marked with red writing. ...3 Figure 3. Map of the areas with deposition and erosion in Mora. Adapted from Mora municipality (2006

& 2017). (Esri, DeLorme, HERE & MapmyIndia) ...4 Figure 4. Study area location in Europe and Sweden with marked rivers, lakes and islands (Esri,

DeLorme, HERE & MapmyIndia). ... 10 Figure 5. Bathymetry map for the reach. The depth is ranging from 0-2 (light) to 10-12 (dark) ( (SMHI, 2000). ... 12 Figure 6. Map showing the two SMHI measuring stations for hydrological data in Österdalälven

(Spjutmo) and Oreälven (Skattungen) (Esri, DeLorme, HERE & MapmyIndia). ... 13 Figure 7. A conceptual model showing the discharge and water surface elevation boundary conditions.

The boxes represent inlets and outlets, and the arrows represent the flux direction. The dashed line marks the model domain. BC: Boundary Condition (Esri, DeLorme, HERE & MapmyIndia). ... 18 Figure 8. The final mesh split in two parts where the left part is the north part and the right the south part.

The black dotted line marks the I-line from which result was extracted. The red dashed box marks the area where the groynes were located. ... 24 Figure 9. Water surface elevation [m]for one of the groyne configurations 45/6 (left) and standard

configuration (right) for Q=100m³/s. ... 26 Figure 10. Simulation results showing the uniformly scaled velocity vector field [m/s] for the standard configuration for Q=100 m³/s marked by regions a-f. ... 27 Figure 11. Velocity field in area e, with overlaid eddy viscosity layer [m²/s] for the standard configuration for Q=100 m³/s. Circulation and reversal flow regions are apparent. ... 28 Figure 12. Velocity vector field [m/s] with reverse flow in east side of the channel in area d for the

standard configuration for Q=100m³/s. ... 29 Figure 13. Distribution of bed shear stress [N/m²] for the standard configuration for Q=100 m³/s... 30 Figure 14. Velocity variation for varying flow discharges in Österdalälven along the constant I-line marked in Figure 8 for the standard configuration. ... 31 Figure 15. Shear stress variation for varying flow discharges in Österdalälven along the constant I-line marked in Figure 8 for the standard configuration. ... 31 Figure 16. Velocity field [m/s] in area e, for the standard configuration for Q=200 m³/s. ... 32 Figure 17 Sediment transport rate for the suspended load and bed load for the standard configuration for Q=100m³/s along the I-line marked in Figure 8. ... 33 Figure 18. Normalized sediment transport rate, shear stress, and velocity magnitude for the standard configuration for Q=100m³/s along the I-line marked in Figure 8. ... 33 Figure 19. Bed level changes [m] for the standard configuration Q=100 m³/s after 1 year. ... 34 Figure 20. Sediment yield at outlets after1 year for the standard configuration for varying discharges. ... 35 Figure 21. Sediment yield at west outlet for Q=100m³/s after 1 year with variations in transport capacity formula. The red bar marks the standard configuration. ... 36

v

Figure 22. Sediment yield at west outlet Q=100m³/s after 1 year for variations in the configuration... 36

Figure 23. Uniform vector velocity field [m/s] for configurations with groynes for Q=100 m³/s. The groyne configurations are from top to bottom 4, 6, and 9 groynes... 38

Figure 24. Bed shear stress [N/m²] in Österdalälven for Q=100 m³/s. The groyne configurations are from top to bottom 4, 6, and 9 groynes. ... 39

Figure 25. Bed change [m] in Österdalälven around groynes after 1 year for Q=100 m³/s. The groyne configurations are from top to bottom 4, 6, and 9 groynes. ... 40

Figure 26. Sediment yield at outlets for 1 year for configurations with and without groynes for Q=100 m³/s. The red bar marks the standard configuration. ... 41

Figure 27. Velocity vector field on top of eddy viscosity [m²/s] for Q=100 m³/s with parabolic eddy viscosity turbulence mode (left) and mixing length turbulence model (ri ... 42

List of tables

Table 1. Annual suspended sediment yield and load for two measuring stations in Dalälven. The volume of sediment is calculated using sediment density ρ=2650 kg/m³. ... 11

Table 2. Particle-size distribution from Klarälven. ... 13

Table 3. Symbol explanations for equations 5-13. ... 17

Table 4. Summary of boundary condition type for the model. ... 19

Table 5. Sediment size class and properties for the initial conditions for the sediment transport model. .. 20

Table 6. Regime coefficient for two stations in Dalälven. ... 20

Table 7. Comparison of sediment load calculated from the model result and sediment load calculated from the regression curves. ... 21

Table 8. Simulation time and time step for the models. ... 23

Table 9. Summary of simulation configurations. ... 23

Table 10. Summary of the sediment transport modes and capacity formulas used in the simulations. ... 23

Table 11. The three groyne configurations used for the simulations. ... 24

Table 12. Sediment yield at the west outlet after 1 year for the standard configuration for Q=100m³/s. ... 35

Table 13. Summary of sediment yield change at the west outlet for 1 year for different configurations. .. 35

Table 14. Change in sediment transport for groynes compared to no groynes, after 1 year for Q=100 m³/s. ... 41

vi

Table of contents

Abstract ...i

Sammanfattning ... ii

Acknowledgements ... iii

List of figures ... iv

List of tables ...v

1. Introduction ...1

1.1. Background and problem statement ...1

1.2. Aims ...5

1.3. Limitations ...5

2. Theoretical background ...5

2.1. Flow and transport characteristics ...5

2.2. Deposition mechanism in river bends ...8

2.3. Modelling ...8

2.4. River training...8

2.5. Groynes...8

3. Method ...9

3.1. Study Area ...9

3.2. Data collection ... 11

1.2. CCHE modelling system ... 14

1.1. Model setup ... 16

1.2. The modelling approach in the CCHE system ... 21

2. Result ... 25

2.1. Standard configuration ... 25

2.2. Application of groynes ... 37

2.3. Turbulence model choice ... 41

2.4. Model validation ... 43

3. Discussion ... 43

3.1. The implication of the results to the prevailing sedimentation problems ... 43

3.2. The possibility of mitigation measures... 44

3.3. Model validity ... 44

3.4. Sensitivity analysis... 45

3.5. The study’s limitations ... 46

vii 4. Conclusions ... 46 5. Bibliography ... 47

1

1. Introduction

This chapter describes the background of the problem, the current situation, and previous research on the problem. Consequentially, it states the purpose and limitations of this study.

1.1. Background and problem statement

The river Österdalälven is a regulated morphologically active river with complicated flow and sediment transport patterns that have a strong dynamic nature. During the past two decades, extensive sediment transport problems have become noticeable along the river reach and at its entrance to the downstream lake Siljan in Mora. Large quantities of fine sediment deposit along the shorelines and into the lake which has caused severe navigation problems as well as significantly reduced the water storage capacity.

Österdalälven has a history of landslides and channelling north of Mora (SOU 2006:94). There are significant unstable sediment deposits at the Österdalälven mouth in Siljan, of which a picture is shown in Figure 1. Österdalälven deposits large quantities of fine sediments when passing the city of Mora,

resulting in a risk of eventually clogging the entry to the lake Siljan. The clogging of the river entry elevates the risk of the river breaking through and forming a new channel. Current measures to mitigate the problem are being undertaken in the form of dredging the river channel (Mora Municipality, 2006).

Areas with sedimentation problems are at the intersection of Oreälven and Österdalälven, in the straight channel after this intersection, and in the main problem area: the outlets to Siljan, see Figure 2 and Figure 3. According to SMHI (2009), as cited by Mora Municipality (2017), the flow velocities in Österdalälven are generally too low for erosion to occur. However, there is a risk for erosion at high flows by the railway bridge, and at the bank at outer bends of the river. There is also a risk for sedimentation in all inner banks of river bends.

A previous study covering Österdalälven by Dutto (2004) investigated how the river regulation had influenced the sedimentation. The study concluded that the river sediment transport capacity along its lower reaches (downstream of Mora) had experienced a significant decrease, compared to the conditions before the river regulation. Consequently, since the regulation the suspended load in the reach has increased from an estimated 40% to 60% of the total sediment load. It was also concluded that the sedimentation rate in Mora harbour has increased significantly, as well as in most of the reaches of Österdalälven upstream of Mora until Spjutmo, for location see Figure 6. As a result of this, the width of the west inlet of Siljan has decreased between the years 1844 and 2000. The same study showed that the regulation in Österdalälven caused an increase of the magnitude of normal discharges while there is a considerable decrease in the magnitude of peak discharge values. One conclusion of the study is that the regulation has resulted in reduced morphological activities.

The present project is an attempt to address some of the foregoing problems using a scientific approach.

2 Figure 1. Photos of the sandbanks by anonymous photographer (personal communication with B. Dargahi, 2018) deposited on the island Sandholmen in Siljan. For the location of the island in the lake, see Figure 4.

3 Figure 2. Map retrieved from B. Dargahi (personal communication, 2018) of the reach showing depth (light to dark blue), areas where dredging (dashed red area), and beach protection have been performed (red dots). The volume of removed sediment is marked with red writing.

4 Figure 3. Map of the areas with deposition and erosion in Mora. Adapted from Mora municipality (2006 & 2017).

(Esri, DeLorme, HERE & MapmyIndia)

5

1.2. Aims

The aims of the project are:

1. To investigate the nature of the flow and sediment transport in the river 2. To analyse the underlying causes of sedimentation

3. Investigate whether sediment mitigation measures can be applied

4. Explore the possibility of creating a working river numerical model despite a lack of relevant field data

1.3. Limitations

The project focus is on cause and effect investigations rather than seeking applicable mitigation measures that would require extensive field data and more complex modelling approach that were possible within the frames of the present limited study.

2. Theoretical background

This section gives a short account of different types of river and sediment transport characteristics as well as modelling as a tool for hydraulic engineering and river training works.

2.1. Flow and transport characteristics

Flow can be characterised by the parameters time and distance. Flow division with respect to time is steady: constant with time: or unsteady, variant with time. Flow division with respect to distance is uniform: where the flow cross-section area is constant along the flow path, or non-uniform: where the flow cross-section area changes. For steady state flow through a control volume, the mass influx equals the mass efflux in a continuity equation. For unsteady state through a control volume, the mass influx equals the mass efflux plus the mass change within the control volume. These continuity equations can also be applied to change in momentum (Dey, 2014).

Fluid flows can also be characterized by the way they flow. Fluid flows can be laminar or turbulent.

Laminar flows are predictable with slow mixing and can be described as layers of fluid flowing on top of each other. Turbulent flows are unpredictable with fast mixing, chaotic flow directions and the forming of eddy currents (Dey, 2014). Turbulence in fluid dynamics is described by different models, where the k- epsilon the most common. The k-epsilon is a two-equation, linear eddy viscosity Reynold averaged Navier Stokes approach. The k-epsilon 2-equation model has been shown to be a robust model. It can, however, be sensitive to mesh quality (Autodesk, 2018). Other simpler turbulence models are the eddy viscosity parabolic model and the eddy viscosity mixing length model. These two models can be more stable than the k-epsilon model. The eddy viscosity model is best suited for flows with low velocity. The mixing length model is not suited for flows with boundary layer separation or recirculation (Argyropoulus

& Markatos, 2014).

6 ---

The following two sections are reported directly from the book chapter Reservoir Sedimentation by the permission of the author (Dargahi, 2012).

2.1 Sediment transport

The sediment transport process in a river is a result of a complex interaction between the various sediment transport processes that prevail in the river and as well as the hydrodynamics of the river. To understand the sedimentation process one must consider the process in two interrelated stages: (1) the motion of sediment particles, and (2) the river channel sediment transport characteristics. All these processes are controlled by a large number of flow parameters, soil or sediment properties, basin properties, and the hydrological variables.

The motion of sediment particles is caused by the combined action of the gravity force working on the sediment particles and the entrainment of sediment particles by flow forces. The latter are the

hydrodynamic forces that act upon the particle, producing drag and lift forces. The sediment particles will remain in an equilibrium state as long as the critical particle shear stress is not exceeded. Under increasing flow velocity the magnitude of the flow forces will exceed the critical shear stress and the particles start to move. The critical shear stress (τcr) is commonly determined using the Shield (1936) diagram that relates the shear stress to the particle Reynolds number ( u*Dm/ν). The relationship reads:

……….…………(5)

in which g=acceleration of gravity, ρs= sediment density, ρ=water density, u*=shear velocity

(hydrodynamic force), and Dm=characteristic sediment diameter. The critical shear stress can also be written in terms of critical shear velocity as ρuc*2. Equation 5 is one of the most important relationships

2.2 River sediment transport processes

In their natural environment, all rivers display a number of classical features, among which are a

meandering of the river channel and the formation of different types of river beds (i.e., ripples, dunes, and anti-dunes and the formation of various types of sand banks and bars. The river channel sediment

transport capacity is controlled by the hydraulics of the flow (applied shear stresses), the sediment properties, and the hydrological variables. The available and supplied sediment to the river undergoes different modes of transport during its path along the river. There are two major transport modes: bed load transport and suspended load transport. Bed load transport is the movement of sediment particles in contact with the bed by rolling, sliding and jumping. Suspended load is transported by the diffusion action of turbulence. The origin of the transported materials is important. The transport that has its origin in a river bed is known as bed-material transport. Here, the transport mode (either bed load or suspended load) is determined by the bed sediment composition and flow conditions. The external supply of materials

) ) (

(

*









_m

s

cr u D

g = f

−

7 (surface erosion) is known as wash load and is not directly related with the river channel flow. Wash loads are normally composed of very fine to coarse silt (4 µm - 60 µm) that is transported in suspension.

To distinguish between the two material origins is of importance for reservoir sedimentation. Wash load is the main contributor from the river to the reservoir sedimentation. Surface erosion models are needed to estimate the wash load. The annual suspended sediment yield of the major rivers in the world is reported to be 20x10⁹ tons (Holeman, 1968). Table 3 gives a summary of the annual sediment loads and the sediment yields for 10 major rivers in the world (Allen, 1997). It is interesting to note that the sediment yield from the Amazon River basin is relatively low compared to its drainage area and to other major rivers such as the Colorado River and the Ganges River. A major part of the Amazon basin is covered with dense tropical forest that limits the sediment yield from the basin.

Table 3 Annual sediment yield and suspended sediment for 11 major rivers (Allen 1997)

The three other important sources of sediment are riverbank erosion, landslides, and reservoir shoreline erosion. In many cases, riverbank erosion is a natural process that is partly related to the meandering of the river. Figure 2 shows an example of riverbank erosion in the upper river reach of Klarälven, which enters Sweden in the north of the county of Värmland. Riverbank erosion can in some cases be the major contributor to the total sediment load in a river.

River Drainage area (km²)

Mean flow discharge (m³/s)

Annual sediment yield (t/km² y)

Annual suspended load (Mt/y)

Amazon 6 150 000 200 000 187 1150

Colorado (CA)

640 000 32 234 150

Mississippi 334 400 18 400 120 125

St Lawrence 1 185 000 14 300 4 3

Rhien 225 000 2 243 0.72 17

Volga 1 350 000 8 400 26 19

Niger 1 112 700 6 020 32 29

Nile 2 715 000 317 46 125

Ganges 980 000 11 600 535 524

Yellow 980 00 2 858 120 122

8

2.2. Deposition mechanism in river bends

In a meandering river, and river bends in general, the flow is affected by the centrifugal acceleration resulting in helical flow motion and a super-elevated surface in the transverse direction. Surface flow is directed towards the outer bank and bed flow towards the inner bank. This phenomenon results in gradual erosion of the outer bank and gradual deposit at the inner bank of the following river bend (Dey, 2014). It should be noted that the sediment motion is statistical due to the fluctuating character of the acting forces.

2.3. Modelling

Hydraulic modelling is a tool to simulate natural processes, e.g. in rivers. It can be used to foresee morphological evolution such as scouring or deposition of sediment. Creating a numerical hydraulic model of an object can be easier than performing experiments on the real-world object. Valuable conclusions can be drawn if the model is calibrated and validated with field data.

A numerical model can approximate the physical properties of a real-world object. By using time-step solutions, the numerical problems can be solved so that a converged solution can be reached. A representative numerical model run with good input data can provide meaningful numerical solutions.

However, all numerical models are approximations and are laden with a certain amount of error. These errors are due to physical and mathematical approximations (Zang, 2006).

2.4. River training

River training is a method where one can change the courses of natural river processes by constructing physical features that modify the flow characteristics. The goal of river training is to improve the state of the river including its bottoms and banks, mitigate or prevent floods, reduce sediment transport and erosion, and enable navigation and passing. There are many different kinds of physical river training structures, which can be divided into two categories: longitudinal and transversal to the main flow direction. Longitudinal structures are usually levees or different kinds of bank reinforcement. Transversal structures can be check dams, sills, or groynes (Shresta, GC, Adhikary, & Rai, 2012). The choice and design of a training structure depend on criteria such as purpose and effect, flow and bank characteristics, available material, maintenance need, and costs (U.S. Army Corps of Engineers, 2002, 2006). A useful and frequently employed river training method is morphological modification of a river reach using groynes.

2.5. Groynes

Groynes (also referred to as groins, spur dykes, bendway weirs, etc.) are transversal structures for river training. They are widely used for bank protection and erosion control. Groynes are direct erosion

mitigation measures that are constructed at an angle to the major flow direction, stretching from the banks into the river. Groynes can be at angle towards upstream, downstream, or orthogonal to the flow direction or the bank. Groynes can be permeable or impermeable. They can be constructed as submerged or emerged structures, usually relative to the top of the bank. They can be constructed from rocks, concrete, wood, sand, or other material. Groynes are often installed in groups consisting of several groynes installed

9 in a row with a certain distance between (U.S. Department of the Interior, 2015). The group of groynes is referred to as groyne field or groyne system. Groynes can be used to prevent sediment accretion in areas downstream of the groynes them (U.S. Army Corps of Engineers, 2008). By installing a group of groynes, the major flow field is directed away from the bank. By creating a zone of lower velocity in the groyne field, sediment can be deposited between the groynes on the upstream side of each groyne. Eddy currents will form in the groyne field, and energy is dissipated. Some erosion may take place on the downstream side of the groynes, as well as at the tips of the groins, forming so-called scour holes. The erosion is usually initially large and diminishes with time (U.S. Department of the Interior, 2015).

Groyne design has been conducted by engineering experience and rule of thumbs rather than by standard design criteria, as this is yet to be conceived. There are, however, some existing guidelines where most commonly used are the Coastal Engineering Manual (CEM), published by the U.S. Army Corps of Engineers (U.S. Army Corps of Engineers, 2002, 2006) when local design standard are missing (Odén &

Johansson, 2005). Design characteristics of groynes include orientation angle, groyne length, spacing ratio, permeability, width, and slope. The spacing ratio is defined as the ratio between the arc length between groins and the longitudinal distance of the groyne, see Equation 1. According to CEM, a value of 2-3 is accepted as an initial value for groyne design.

𝑆 = ^{𝐿𝑎𝑟𝑐}

𝐿𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 (1)

A value of the spacing ratio close to 1 will render a single eddy current in the groin field, a value between 2 and 4 will render two currents, and a larger value than 4 will result in penetration of the main flow field into the groin field (Youssef & de Vriend, 2010). According to Julien & Duncan (2003), the spacing should not exceed 4 as this will decrease the size of the low-velocity zone.

3. Method

This section includes a description of the study area and the complete approach to set up and run the model, as well as a general description of the modelling system CCHE2D.

3.1. Study Area

Österdalälven is a 300 km long section of Dalälven between Idre and Djurås, where it combines with Västerdalälven forming Dalälven. As the river Österdalälven reaches the city of Mora, it flows into the lake Siljan. The upstream lake Orsasjön is connected to Siljan with the river Oreälven. The location and extensions of the rivers and lakes are presented in Figure 4.

Österdalälven is a regulated river with six hydropower dams, including the largest dam in Sweden, Trängslet. The regulation implies that the magnitude of the flow is regulated and can, in this case, vary between 0 and 250 m³/s. However, a minimum flow magnitude of 21m³/s is set to imitate the natural conditions (Hedström-Ringvall et al., 2017).

10 Figure 4. Study area location in Europe and Sweden with marked rivers, lakes and islands (Esri, DeLorme, HERE

& MapmyIndia).

11

3.2. Data collection

3.2.1. Hydrological data

The available hydrological data for the analysis were:

• Daily discharge values measured at Spjutmo station in Österdalälven ranging from 1996 to 2017.

• Daily discharge values measured at Skattungen station in Oreälven ranging from 1931 to 2017 (SMHI, 2018a).

• A bathymetry map of the reach, see Figure 5.

The locations of the measuring stations are marked in Figure 5 and Figure 6.

1.1.1. Sediment data

In a project conducted by SMHI, sediment data was measured between the years 1967 and 1993 in two stations in Dalälven. The stations were located at the station Vikbyn in Dalälven, approximately 110 km southeast of Mora, and at the mouth of Dalälven in the Bothnian sea in Älvkarleby. Analyses of these measurements show that the amount of suspended and soluble solids was correlating well with the flow magnitude in between the years of 1967-1993 (Brandt, 1996). For this project, the average flow and annual sediment yield, listed in Table 1, have been produced from the measured data in these two stations. These stations are located downstream of this project’s study area.

Table 1. Annual suspended sediment yield and load for two measuring stations in Dalälven. The volume of sediment is calculated using sediment density ρ=2650 kg/m³.

Measuring station

Drainage area [km²]

Mean flow discharge [m³/s]

Annual suspended sediment yield per km² [tonnes/km² y]

Annual suspended sediment yield [ktonnes/y]

Annual suspended sediment yield [m³]

Vikbyn 25 950 312 3.8 99 37 470

Älvkarleby 28 959 347 1.8 53 19 830

Apart from the limited and general data from Dalälven listed in Table 1, no field data concerning sediment load or sediment size distributions in Österdalälven were available to this study. It is known from previous studies (Dargahi, 2006) in morphologically similar river that the sediment consists mostly of sand. Sediment data which was available was field measurements from the lower reaches of Klarälven which is a relatively large river flowing south-west of Dalälven. The soil types in the watersheds of Klarälven and Dalälven are similar (SMHI, 2018b).

The field sediment data from Klarälven consists of various soil samples in the form of particle -size distributions in graph form (Dargahi, 2006). One sample is presented in Table 2, where the values have been noted in the table by the author. The average size of this material sample is of the category fine sand.

12 Figure 5. Bathymetry map for the reach. The depth is ranging from 0-2 (light) to 10-12 (dark) ( (SMHI, 2000).

13 Figure 6. Map showing the two SMHI measuring stations for hydrological data in Österdalälven (Spjutmo) and Oreälven (Skattungen) (Esri, DeLorme, HERE & MapmyIndia).

Table 2. Particle-size distribution from Klarälven.

Grain size [mm]

% less than indicated size

2 100

1 90

0.6 45

0.3 5

0.125 1

0.08 0

14

1.2. CCHE modelling system

The CCHE modelling system used in this study is a system for modelling free surface flows, sediment transport, and morphological processes. This modelling system was chosen since it is well suited for the aim of the study of modelling hydraulic and sediment transport mechanisms.

The system includes three parts: a structured mesh generator CCHE-MESH, the CCHE2D flow and transport model, and a graphical user interface CCHE-GUI. The software is developed by the National Center for Computational Hydroscience and Engineering (NCCHE) (Zang, 2006). The most important features of this software for this study are described below. Full documentation of the CCHE modelling system can be found in the CCHE documentation (Zang, 2006). CCHE-MESH is a software for

generating structured meshes in 2D. Topography databases are used to generate algebraic and numerical meshes. The software can also be used to create the topography databases needed for the mesh generation.

The CCHE2D model is a depth-averaged two-dimensional numerical model for hydrodynamic and sediment transport modelling in unsteady open channel flows over loose beds (Zhang & Jia, 2009).

1.2.1. Hydrodynamic model and governing equations

The governing equations for solving an initial boundary value problem in the hydrodynamic model are the depth-averaged Navier-Stokes equations for continuity (Equation 2) and momentum in two

dimensions (Equations 3-4):

Continuity equation:

𝛿𝑍

𝛿𝑇+^{𝛿(ℎ𝑢 )}

𝛿𝑥 +^{𝛿(ℎ𝑣)}

𝛿𝑦 = 0 (2)

Momentum equations:

𝛿𝑢 𝛿𝑡 + 𝑢^𝛿𝑢

𝛿𝑥+ 𝑣^𝛿𝑢

𝛿𝑦= −𝑔^𝛿𝑍

𝛿𝑥+¹

ℎ[^{𝛿(ℎ 𝜏𝑥𝑥)}

𝛿𝑥 +^{𝛿(ℎ𝜏𝑦𝑥)}

𝛿𝑦 ] −^𝜏𝑏𝑥

𝜌ℎ + 𝑓_𝐶𝑜𝑟𝑣 (3)

𝛿𝑣 𝛿𝑡+ 𝑢^𝛿𝑣

𝛿𝑥+ 𝑣^𝛿𝑣

𝛿𝑦= −𝑔^𝛿𝑍

𝛿𝑦+¹

ℎ[^{𝛿(ℎ𝜏𝑦𝑥)}

𝛿𝑥 +^{𝛿(ℎ𝜏𝑦𝑦)}

𝛿𝑦 ] −^𝜏𝑏𝑦

𝜌ℎ + 𝑓_𝐶𝑜𝑟𝑢 (4)

, in which u and v are the depth-integrated velocity components in the x- , and y- directions, g is the gravitational constant, Z is the water surface elevation, h is the local water depth, 𝜏_𝑥𝑥, 𝜏_𝑦𝑥, 𝜏_𝑥𝑦 , 𝜏_𝑦𝑦 are the depth-integrated Reynolds stresses, 𝜌 is the water density, 𝜏_𝑏𝑥 and 𝜏_𝑏𝑦 are the bed surface shear stress, and 𝑓_𝐶𝑜𝑟 is the Coriolis’ parameter (Zang, 2006).

The available turbulence models are two eddy viscosity models: the depth-integrated parabolic model and the mixing length model, and the 2-equation k-epsilon model.

15

1.2.2. Sediment transport model

The CCHE2D sediment transport model employs a non-equilibrium model for both bed and suspended load. Using a non-equilibrium model has been shown to be needed for cases with strong deposition, especially under unsteady flow conditions.

The CCHE2D sediment transport model has the option of treating either combined sediment transport or transport separated as bed load or suspended load. The user can choose from three types of transport modes:

1. Total load as suspended load plus bed load 2. Total load as suspended load

3. Total load as bed load.

All three transport modes take both suspended load and bed load into consideration. However, the two latter modes compute the total load but with either suspended load or bed load as the dominant transport mode. For these two transport modes, four transport capacity formulas are available:

• Wu et. al.

• Modified Engelund& Hansen

• Modified Ackers& White

• SEDTRA module

The governing equations for sediment transport and bed deformation for the three transport modes are presented below. Symbol explanations are listed in Table 3. For full documentation and all derivations, the reader is directed to the CCHE2D sediment transport model manual by Wu (2001).

Total load as suspended load plus bed load

Bed load and suspended load transport are given by equations 5&6 respectively:

𝛿(𝜹𝑐̅_𝑏𝑘)

𝛿𝑡 +^{𝛿𝑞𝑏𝑘𝑥}

𝛿𝑥 +^{𝛿𝑞𝑏𝑘𝑦}

𝛿𝑦 + ¹

𝐿_𝑡(𝑞_𝑏𝑘− 𝑞_𝑏∗𝑘) = 0 (5)

𝛿(ℎ𝐶_𝑘)

𝛿𝑡 +^{𝛿(𝑈ℎ𝐶𝑘)}

𝛿𝑥 +^{𝛿(𝑉ℎ𝐶𝑘)}

𝛿𝑦 = ^𝛿

𝛿𝑥(𝜀_𝑠ℎ^𝛿𝐶𝑘

𝛿𝑥) + ^𝛿

𝛿𝑦(𝜀_𝑠ℎ^𝛿𝐶𝑘

𝛿𝑦) + 𝐸_𝑏𝑘 − 𝐷_𝑏𝑘 (6)

Bed deformation is computed from the equation 7 or the sediment continuity equation 8:

(1 − 𝑝^′)^{𝛿𝑧𝑏𝑘}

𝛿𝑡 = 𝛼𝜔_𝑠𝑘(𝐶_𝑘 − 𝐶_∗𝑘) +^{(𝑞𝑏𝑘−𝑞𝑏∗𝑘)}

𝐿_𝑡 (7)

(1 − 𝑝^′)^{𝛿𝑧𝑏𝑘}

𝛿𝑡 +^{𝛿(ℎ𝐶𝑡𝑘)}

𝛿𝑡 +^{𝛿(𝑞𝑏𝑘𝑥+𝑞𝑠𝑘𝑥)}

𝛿𝑥 +^{𝛿(𝑞𝑏𝑘𝑦+𝑞𝑠𝑘𝑦)}

𝛿𝑦 = 0 (8)

16 Total load as bed load

Bed load transport is given by equation 9:

𝛿(ℎ𝐶_𝑡𝑘)

𝛿𝑡 +^{𝛿(𝛼𝑡𝑥𝑞𝑡𝑘)}

𝛿𝑥 +^{𝛿(𝛼𝑡𝑦𝑞𝑡𝑘)}

𝛿𝑦 + ¹

𝐿_𝑡(𝑞_𝑡𝑘− 𝑞_𝑡∗𝑘) = 0 (9)

Bed deformation is computed from the sediment continuity equation 10 or equation 11:

(1 − 𝑝^′)^{𝛿𝑧𝑏𝑘}

𝛿𝑡 +^{𝛿(ℎ𝐶𝑡𝑘)}

𝛿𝑡 +^{𝛿(𝑞𝑏𝑘𝑥+𝑞𝑠𝑘𝑥)}

𝛿𝑥 +^{𝛿(𝑞𝑏𝑘𝑦+𝑞𝑠𝑘𝑦)}

𝛿𝑦 = 0 (10)

(1 − 𝑝^′)^{𝛿𝑧𝑏𝑘}

𝛿𝑡 =^{(𝑞𝑡𝑘−𝑞𝑡∗𝑘)}

𝐿_𝑡 (11)

Total load as suspended load

Suspended load transport is given by equation 12:

𝛿(ℎ 𝐶_𝑡𝑘)

𝛿𝑡 +^{𝛿(𝑈ℎ 𝐶𝑡𝑘)}

𝛿𝑥 +^{𝛿(𝑉ℎ𝐶𝑡𝑘)}

𝛿𝑦 = ^𝛿

𝛿𝑥(𝜀_𝑠ℎ^{𝛿𝐶𝑡𝑘}

𝛿𝑥 ) + ^𝛿

𝛿𝑦(𝜀_𝑠ℎ^{𝛿𝐶𝑡𝑘}

𝛿𝑦 ) + 𝛼𝜔_𝑠𝑘(𝐶_𝑡∗𝑘− 𝐶_𝑡𝑘 ) (12)

Bed deformation is computed from the sediment continuity equation 13:

(1 − 𝑝^′)^{𝛿𝑧𝑏𝑘}

𝛿𝑡 = 𝛼𝜔_𝑐𝑘(𝐶_𝑡𝑘 − 𝐶_𝑡∗𝑘) (13)

1.1. Model setup

1.1.1. Conceptual model

The model area will include a bend of Österdalälven which intersects with Oreälven in Mora, the section of Oreälven between the lake Orsasjön and Siljan, the mouths of Oreälven and Österdalälven into Siljan, and the most northern part of Siljan. The outlet at Siljan is divided into two by the islands Klubbholmen and north and south Gotholmen. There is also another island, Sandholmen, in the southern part of the outlet. The location of the lakes, the rivers, and the island are marked in Figure 4. The inlets are referred to as Oreälven inlet and Österdalälven inlet. The outlets are referred to as the south and west outlet. These inlets and outlets define the model’s two boundary conditions. A conceptual representation of the model is shown in Figure 7.

The boundary conditions at the inlets define the water and sediment discharge. The water surface elevation is defined by the boundary conditions at the two outlets. The bed and banks of the river are no- flow boundaries, i.e. the groundwater exchange is negligible.

17 Table 3. Symbol explanations for equations 5-13.

 Ratio between near-bed concentration and depth-averaged concentration

Lt Adaptation length of bed-material load

tx Direction cosine of total load transport 𝑝’ Porosity of bed material 𝐶_𝑘 Depth-averaged suspended-load

concentration

𝑞_𝑏𝑘 Bed load transport rate of the k:th sediment size class

𝐶_𝑡𝑘 Depth-averaged concentration of the total load

𝑞_𝑏∗𝑘 Bed load transport of the k:th sediment size class at the interface between the suspended- load zone and bed-load zone

𝐶_𝑡∗𝑘 Depth-averaged transport capacity of total load

𝑞_𝑏𝑘𝑥 𝑞_𝑏𝑘𝑦

Bed load transport in the x or direction of the k:th sediment size class

𝐶_∗𝑘 Depth-averaged concentration under equilibrium conditions

𝑞_𝑠𝑘𝑥 𝑞_𝑠𝑘𝑥

Suspended load transport rate in x-, or y, direction

𝑐̅_𝑏𝑘 Average concentration of bed load at the bed-load zone

𝑞_𝑡𝑘 Actual transport rate of the k:th sediment size class of bed-material load

𝜀_𝑠 Eddy diffusivity of sediment 𝑞_𝑡∗𝑘 Actual transport capacity of the k:th sediment size class of bed-material load

 Thickness of bed load zone U, V Depth-average flow velocities in x- or y- directions

𝐸_𝑏𝑘 Entrainment flux of the k:th sediment size class at the interface between the suspended-load zone and bed-load zone

𝜔_𝑠𝑘 Settling velocity of the k:th sediment size class

Dbk Deposition flux of the k:th sediment size class at the interface between the suspended-load zone and bed-load zone

𝑧_𝑏𝑘 The thickness of bed over datum

h Local water depth

1.1.1. Initial conditions for the hydrodynamic model

Initial conditions include conditions for the flow and the bed. The initial conditions for the flow are initial water surface elevation and bed elevation which were inferred from the bathymetry map in Figure 5. The initial conditions for the bed include bed roughness, erodibility, max deposition thickness, max erosion thickness, layer thickness, and layer sample number. These parameters were unknown in this study. The bed roughness was estimated to n=0.025. The maximum deposition and erosion thickness were set so that deposition and erosion thicknesses were unlimited. The remaining parameters were left as the default values provided by the modelling system.

18 Figure 7. A conceptual model showing the discharge and water surface elevation boundary conditions. The boxes represent inlets and outlets, and the arrows represent the flux direction. The dashed line marks the model domain.

BC: Boundary Condition (Esri, DeLorme, HERE & MapmyIndia).

19

1.1.2. Boundary conditions for the hydrodynamic model

The setup of the boundary conditions is listed in Table 4.

Table 4. Summary of boundary condition type for the model.

Hydrodynamic model Sediment transport model Inlet boundary Österdalälven

Oreälven

Water discharge:

Steady inflow or hydrograph

Sediment discharge (bed load and suspended load):

Steady inflow or hydrograph Outlet boundary Siljan Water surface elevation:

Constant value or rating curve

The discharge data used here for the Oreälven inflow is collected upstream in the river at the measuring station Skattungen upstream of Orsasjön as marked in Figure 6. Oreälven is the only main tributary to Orsasjön and can, therefore, be used as the outflow discharge of Orsasjön.

Since water surface elevation data for the outlet at northern Siljan was unavailable, steady-state simulations with varying flow discharges were done to obtain a rating curve for the outlet boundaries.

The used flow discharges were ranging between 30 and 200 m³/s in Österdalälven. Simulations were performed until converged solutions were reached. Two linear rating curves were estimated from these simulations, one corresponding to a higher water surface elevation and one to a lower. However, a range of different rating curves could be fitted, as the model would converge with different outlet surface elevations for the same flows. The rivers and lakes are regulated meaning several discharges can correspond to a single water level and vice versa. The resulting rating curves were Equation 14 for high water surface elevation and Equation 15 for low water surface elevation, where y is the water surface elevation in meters above a datum of 149.7 m a.s.l. and Q the water discharge in m³/s.

𝑦 = 0.0035𝑄 + 11.361 (14)

𝑦 = 0.005𝑄 + 10.169 (15)

The rating curves were developed for the sake of this project only and should not be seen as a representative rating curve for other applications outside of this project.

1.1.3. Parameters and initial conditions for the sediment transport model

The sediment material properties of size class and porosity are listed in Table 5. The simulations were done with a uniform material sediment load. The number of bed layers was set to one for simplicity. The minimum mixing layer thickness was left as the default value. The foregoing choices were the result of unavailable field data.

20 Table 5. Sediment size class and properties for the initial conditions for the sediment transport model.

Size class Mean diameter [mm] Fraction Porosity

1 0.36 1 0.4

The transport mode for the sediment transport can be set to three transport modes: bed load only, suspended load only, and total transport mode, as described in section 1.2. The majority of the simulations were run with the total load mode.

1.1.4. Boundary conditions for the sediment transport model

The boundary conditions for the sediment model are suspended and bed load sediment discharge at inlets, see Table 4. Because the sediment loads were unknown, the sediment load discharge was initially

calculated using the Van Rijn 1984a formula for total load transport, with the help of a program

developed by B. Dargahi (personal communication, 2018). The loads were calculated using the result of the hydrodynamic model at one flow section at each inlet using the rating curve in equation 14. This was done for a low, medium, and high flow relative to the Österdalälven flow.

Dargahi (1984) produced two regression curves for the Vikbyn and Älvkarleby stations in Österdalälven, see equation 16 and Table 6 for regime coefficients:

𝑄_𝑆 = 𝐴𝑄^𝐵 (16)

, where Qs is the solid discharge expressed in tonnes/month, Q discharge in m³/s and A, B are regime coefficients.

Table 6. Regime coefficient for two stations in Dalälven.

A B r

Year 1979/1980 1979/1980 1979/1980

Vikbyn 0.04/0.51 1.98/1.52 0.79/0.56

Älvkarleby 0.01/0.05 2.06/1.82 0.82/0.65

The sediment load calculated by these regression curves were included for the sake of comparison with the calculated sediment transport loads from the model result, see Table 7.

Sediment rating curves were developed from the loads calculated with the Van Rijn formula. The

sediment curves for the two inlets are as shown in equations 17 and 18, in which Qs is in kg/s, and Q is in m³/s.

Österdalälven: 𝑄_𝑠 = 0.0001𝑄 − 0.0032 (17)

Oreälven: 𝑄_𝑠 = 0 (18)

21 Table 7. Comparison of sediment load calculated from the model result and sediment load calculated from the regression curves.

Measuring station

Q [m³/s]

Van Rijn sediment load [kg/s]

Vikbyn 1979 Regression result [kg/s]

Vikbyn 1980 Regression result [kg/s]

Älvkarleby 1979 Regression result [kg/s]

Älvkarleby 1980 Regression result [kg/s]

Österdalälven 50 0.0032 0.035 2.1 0.012 0.024

100 0.0057 0.14 11 0.050 0.083

150 0.014 0.31 29 0.12 0.17

Oreälven 20 0.00 0.0057 0.24 0.0018 0.0044

25 0.00 0.0089 0.41 0.0029 0.0066

30 0.00 0.013 0.63 0.0042 0.0093

The calculated sediment loads shown in Table 7 were low so that for simplicity, the inlet boundary of sediment discharge was set to zero.

1.1.5. Groyne design

The groynes were defined in CCHE2D as thin walls along the selected grid lines. No characteristics such as width or side slopes can be defined, as the structures are single mesh line structures. Different

arrangements of groynes were tested. The varied parameters were the number of groynes and their longitudinal length.

1.2. The modelling approach in the CCHE system

The modelling approach is described below in this section. Creating the models was an iterative process where parameters such as mesh size and boundary conditions were altered, and the model was rerun several times.

1.2.1. Mesh creation from the bathymetry map using CCHE-MESH

A topography database was created in CCHE-MESH by mapping the elevation lines from the bathymetry map in Figure 5. An algebraic mesh was then created, in order to create the final numerical mesh, which is shown in Figure 8. Finally, the topography was interpolated using triangulation interpolation. The mesh quality was evaluated from the parameters smoothness and orthogonality. Several numerical methods are available for generating the numerical mesh. The numerical method which generated the most satisfactory result in terms of the evaluated parameters was chosen which was the numerical RL orthogonal mesh with smoothness control [1]. This numerical method is also recommended by Zhang & Jia (2009) for natural rivers with irregular boundaries.

Triangulation interpolation was chosen as it rendered results that were the most concordant with the bathymetry in between data points. The interpolated bed topography was smoothed in some areas. The mesh was later refined in order to be able to capture flow directions at certain points such as bends, the

22 island, and around the groynes. The final mesh size was I*J= 81*301, where I stretches in the north-south and direction and J in the west-east direction.

1.2.2. The building of a hydraulic model in CCHE2D and hydrodynamic simulations

The mesh was imported into CCHE-GUI, where the hydrodynamic model was set up by defining the boundary and initial conditions. Some initial conditions were unknown in this study; thus, they were estimated in the initial simulations.

The model was run for steady flow discharges in Österdalälven of 50, 100, 150, and 200m³/s. The Q=100m³/s roughly corresponds to the mean flow in Österdalälven at the Spjutmo measuring station (which is 90 m³/s), for location see Figure 6. The corresponding discharge in Oreälven was inferred by calculating the average flow in Oreälven corresponding with the stated discharges in Österdalälven.

A steady-state boundary condition hydrodynamic model was built and ran until a converged solution was found. Convergence is here defined to when the solutions are independent of time. The simulation time was 48 hours divided into two simulation intervals, see Table 8. The time step was chosen so that the model was stable and converging, while not requiring unnecessary long simulation times.

When using a mesh with external boundaries corresponding to the extension of the bathymetry map, the initial simulations showed that the water was flowing in the wrong direction at the Oreälven inlet. The problem was due to the flat bed slope and shallow areas in the river. To overcome this problem, the model was elongated in an upstream direction with a constant depth channel. This moved the boundary further away from the actual model area. This modification gave a reasonable flow condition corresponding to an inward direction of the water flow at this boundary in accordance with the physics.

1.2.3. Sediment transport simulation

The sediment transport model was run coupled with the hydrodynamic model. The simulation time was one year divided into three simulation intervals, see Table 8. The simulations were done under a steady state inflow.

Simulations with several different setups of both the hydrodynamic and sediment transport model were done. The setup with which the simulations for various discharges were made will be referred to as

“standard configuration”. The other configurations were done with Q=100 m³/s, for solely comparison.

The turbulence model, wall slip coefficient, Manning’s roughness coefficient, mesh size, and sediment size were varied one at a time in the purpose of a sensitivity analysis to the choice of these parameters.

Values of boundary conditions and the transport mode choice were calibrated against the measured volume of transported sand at the outlets which are marked in Figure 2, as well as varied for being

included in the sensitivity analysis. The sensitivity analysis was done by comparing the model response to the varied input in comparison to that of the standard configuration in a one-at-a-time approach.

23 Table 8. Simulation time and time step for the models.

Model Simulation time

[s]

Time step [s]

Runs [-]

Total run time [days]

Hydrodynamic 100 000 100 2 2

Sediment transport 1 544 500 10 3 365

Table 9 summarizes the different simulation configurations used in this study. The configurations for the sediment transport modes and capacity formulas are listed by Table 10.

Table 9. Summary of simulation configurations.

Parameter Standard configuration

Setup Variations Turbulence

model option

K-epsilon model Parabolic eddy viscosity model

Mixing length model

Wall slipness coefficient [-]

0.5 0 1

Outlet water surface elevation for Q=100m³/s [m]

10.8,

rating curve in equation 14.

11.8, rating curve in equation 15.

Manning’s roughness coefficient [-]

0.025 0.02 0.03

Mesh Size [I*J] 81*301 49*293 Sediment size

[mm]

0.036 0.6

Table 10. Summary of the sediment transport modes and capacity formulas used in the simulations.

Standard configuration

Setup variations Transport

mode

Total load as suspended and bed load

Total load as suspended load Total load as bed load Transport

capacity formula

Wu et. Al. Modified Ackers and White

Modified Engelund and Hansen

SEDTRA

Simulations with groynes

Groynes were added to the model at the Österdalälven reach near the inflow boundary. The location is marked in Figure 8. Three different configurations were examined, see Table 11, and simulations were done for a simulation time of 1 year for Q=100 m³/s. The spacing ratio was set to 3.

24 Table 11. The three groyne configurations used for the simulations.

Groyne configurations no/ longitudinal length [m]

4/70 6/45 9/30

Figure 8. The final mesh split in two parts where the left part is the north part and the right the south part . The black dotted line marks the I-line from which result was extracted. The red dashed box marks the area where the groynes were located.

25

2. Result

This section will cover the main result of some of the simulations, i.e. velocity vectors, shear stress distributions, bed level changes, and sediment transport characteristics. The result is mainly from the simulations with the standard configuration and groyne configurations for Q=100 m³/s.

2.1. Standard configuration

2.1.1. Result from the hydrodynamic model

The simulated water surfaces at the inlets are 10.9m which means there is a difference of 0.1m between inlets and outlets, resulting in a slope of the water surface elevation of 10^-5. The water surface elevation is shown in Figure 9. The flow division between the west and south outlet is 36% at the west outlet and 64%

at the south outlet in average from simulations with Q=50, 100, 150 and 200m³/s at the Österdalälven inlet.

The flow velocity vector field is presented in Figure 10 for Q=100m³/s. From this result, it can be seen that the flow velocity in area a is low. The flow velocity in area b is higher, especially at the outer part of the river bend. Circulation occurs in area c at the flow intersection region of the two river branches, see Figure 11. There is also circulation in area e where the flow divides to the two outlets, and after the island Sandholmen. Sections with reversed flow occur on the east bank in areas d and e, see Figure 11 and Figure 12. The flow is subcritical throughout the model, i.e. the Froude number is less than 1. As can be seen in Figure 11, the eddy viscosity is large in areas with circulation.

26 Figure 9. Water surface elevation [m]for one of the groyne configurations 45/6 (left) and standard configuration (right) for Q=100m³/s.

27 Figure 10. Simulation results showing the uniformly scaled velocity vector field [m/s] for the standard configuration for Q=100 m³/s marked by regions a-f.

28 Figure 11. Velocity field in area e, with overlaid eddy viscosity layer [m²/s] for the standard configuration for Q=100 m³/s. Circulation and reversal flow regions are apparent.

29 Figure 12. Velocity vector field [m/s] with reverse flow in east side of the channel in area d for the standard

configuration for Q=100m³/s.

Distribution of bed shear stresses

The values of the bed shear stresses are large in areas b, c, and d, see Figure 13, in comparison with the other regions of the model. The bed shear stress correlates well with the velocity field, i.e. the shear stresses are large in areas with high velocity and vice versa, as it can be seen in Figure 14, Figure 15, and Figure 18. The results in these figures are extracted along an I-line of which the location is marked in Figure 8. The marked I-line stretches along the modelled river reach in the middle of the river channel from the intersection of the rivers to the south outlet through areas c-f.

30 Figure 13. Distribution of bed shear stress [N/m²] for the standard configuration for Q=100 m³/s